What is a multidimensional function?
I've just started with multivariable caculus and I wondered what exactly a multidimensional function is.
In general a function might be defined as $f: \mathbb{R}^n \mapsto \mathbb{R}^m $. This function has a multidimensional domain and a multidimensional codomain.
So if someone is just talking about a multidimensional function is they referring to the domain or to the codomain?
So is $f: \mathbb{R}^n \mapsto \mathbb{R} $ or $f: \mathbb{R} \mapsto \mathbb{R}^m $ considered as an one dimensional function? If they both are multidimensional, does it mean there are multiple combinations of say how a four dimension function is defined (Could you tell me which)?
Example, where I didn't understand what functions are actually meant: I learned that from differentiability follows continuity for one dimensional functions, but it isn't the case for multidimensional functions.
Thanks for your help!
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